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Gases Chapter 5
Become familiar with the definition and measurement of gas pressure.
Learn the gas law and ideal gas equation.
Understand the concept of the partial pressures.
Study the kinetic molecular theory and gas Effusion/Diffusion
Main differences between ideal and real gases.
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2. Elements that exist as gases at 250C and 1 atmosphere
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3. Physical Characteristics of Gases
Gases assume the volume and shape of their containers.
Gases are the most compressible state of matter.
Gases will mix evenly and completely when confined to the same container.
Gases have much lower densities than liquids and solids.
Exerts pressure on its surroundings.
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Figure 5.1a: The pressure exerted by the gases in the atmosphere can be demonstrated by boiling water in a large metal can (a) and then turning off the heat and sealing the can.
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Figure 5.01b: As the can cools, the water vapor condenses, lowering the gas pressure inside the can. This causes the can to crumple.
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Force
Area
Pressure =
Units of Pressure
1 pascal (Pa) = 1 N/m2
1 atm = 760 mmHg = 760 torr
1 atm = 101,325 Pa
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10 miles
0.2 atm
4 miles
0.5 atm
Sea level
1 atm
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Boyle’s Law
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As P (h) increases
V decreases
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Boyle’s Law
P a 1/V
Constant temperature
Constant amount of gas
P x V = constant
P1 x V1 = P2 x V2
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Boyle’s Law*
Pressure  Volume = Constant (T = constant)
P1V1 = P2V2 (T = constant)
V  1/P (T = constant)
(*Holds precisely only at very low pressures.)
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13. As pressure increases, the volume of SO2 decrease
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15. A gas that strictly obeys Boyle’s Law is called an ideal gas.
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A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?
P1 x V1 = P2 x V2
P1 = 726 mmHg
P2 = ?
V1 = 946 mL
V2 = 154 mL
P1 x V1 V2
726 mmHg x 946 mL
154 mL =
P2 =
= 4460 mmHg
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Volume-Temperature Relationship
As T increases
V increases
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Charles's Law
Figure 5.9: Plots of V versus T as in Fig. 5.8 except here the Kelvin scale is used for temperature.
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Charles’s Law
The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.
V = bT (P = constant)
b = a proportionality constant
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Charles’s Law
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A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?
V1/T1 = V2/T2
V1 = 3.20 L
V2 = 1.54 L
T1 = K
T2 = ?
V2 x T1 V1
1.54 L x K
3.20 L =
T2 =
= 192 K
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Avogadro’s Law
V a number of moles (n)
Constant temperature
Constant pressure
V = constant x n
V1/n1 = V2/n2
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Figure 5.18: The effects of increasing the number of moles of gas particles at constant temperature and pressure.
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Ideal Gas Equation
Boyle’s law: V a (at constant n and T) 1 P
Charles’ law: V a T (at constant n and P)
Avogadro’s law: V a n (at constant P and T)
V a nT P
V = constant x = R nT P
R is the gas constant
PV = nRT
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Ideal Gas Law
PV = nRT
R = proportionality constant
= L atm  mol
P = pressure in atm
V = volume in liters
n = moles
T = temperature in Kelvins
Holds closely at P < 1 atm
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The conditions 0 0C and 1 atm are called standard temperature and pressure (STP).
Experiments show that at STP, 1 mole of an ideal gas occupies L.
PV = nRT
R = PV nT =
(1 atm)(22.42L)
(1 mol)( K)
R = L • atm / (mol • K)
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What is the volume (in liters) occupied by 49.8 g of HCl at STP?
T = 0 0C = K
P = 1 atm
PV = nRT
n = 49.8 g x
1 mol HCl
36.45 g HCl
= 1.37 mol
V =
nRT P
V =
1 atm
1.37 mol x x K
L•atm
mol•K
V = 30.6 L
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Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0C is heated to 85 0C at constant volume. What is the final pressure of argon in the lightbulb (in atm)?
PV = nRT
n, V and R are constant nR V = P T
= constant
P1 = 1.20 atm
T1 = 291 K
P2 = ?
T2 = 358 K P1 T1 P2 T2 =
P2 = P1 x T2 T1
= 1.20 atm x
358 K
291 K
= 1.48 atm
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29. Density (d) Calculations
m is the mass of the gas in g m V = PM RT
d =
M is the molar mass of the gas
Molar Mass (M ) of a Gaseous Substance
dRT P
M =
d is the density of the gas in g/L
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30. Gas Stoichiometry
What is the volume of CO2 produced at 370 C and 1.00 atm when 5.60 g of glucose are used up in the reaction:
C6H12O6 (s) + 6O2 (g) CO2 (g) + 6H2O (l)
g C6H12O mol C6H12O mol CO V CO2
1 mol C6H12O6
180 g C6H12O6 x
6 mol CO2
1 mol C6H12O6 x
5.60 g C6H12O6
= mol CO2
0.187 mol x x K
L•atm
mol•K
1.00 atm =
nRT P
V =
= 4.76 L
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5.5

31. Dalton’s Law of Partial Pressures
For a mixture of gases in a container,
PTotal = P1 + P2 + P
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32. Dalton’s Law of Partial Pressures
V and T are constant P1 P2
Ptotal = P1 + P2
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33. PA = nART V PB = nBRT V XA = nA nA + nB XB = nB nA + nB PT = PA + PB
Consider a case in which two gases, A and B, are in a container of volume V.
PA =
nART V
nA is the number of moles of A
PB =
nBRT V
nB is the number of moles of B
XA = nA
nA + nB
XB = nB
nA + nB
PT = PA + PB
PA = XA PT
PB = XB PT
Pi = Xi PT
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A sample of natural gas contains 8.24 moles of CH4, moles of C2H6, and moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)?
Pi = Xi PT
PT = 1.37 atm
0.116
Xpropane = =
Ppropane = x 1.37 atm
= atm
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Water Vapor Pressure
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Bottle full of oxygen gas and water vapor
2KClO3 (s) KCl (s) + 3O2 (g)
PT = PO + PH O 2
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37. Kinetic Molecular Theory of Gases
A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points that is, they possess mass but have negligible volume (V  zero).
Gas molecules are in constant motion in random directions. Collisions among molecules are perfectly elastic.
Gas molecules exert neither attractive nor repulsive forces on one another.
The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy
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38. Kinetic theory of gases and …
Compressibility of Gases
Boyle’s Law
P a collision rate with wall
Collision rate a number density
Number density a 1/V
P a 1/V
Charles’ Law
Collision rate a average kinetic energy of gas molecules
Average kinetic energy a T
P a T
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39. Kinetic theory of gases and …
Avogadro’s Law
P a collision rate with wall
Collision rate a number density
Number density a n
P a n
Dalton’s Law of Partial Pressures
Molecules do not attract or repel one another
P exerted by one type of molecule is unaffected by the presence of another gas
Ptotal = SPi
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Figure 5.19: Path of one particle in a gas. Any given particle will continuously change its course as a result of collisions with other particles, as well as with the walls of the container: The concept of Average Speed
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41.  3RT urms = M The distribution of speeds of three different gases
at the same temperature
The distribution of speeds
for nitrogen gas molecules
at three different temperatures
urms =
3RT M 
Note: M in Kg per mole
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42. The Meaning of Temperature
Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)
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Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.
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Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by virtue of their kinetic properties.
NH4Cl
NH3
17 g/mol
HCl
36 g/mol
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Effusion: describes the passage of gas into an evacuated chamber.
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Effusion:
Diffusion:
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Real Gases
Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).
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48. Figure 5.25: Plots of PV/nRT versus P for several gases (200 K).
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Figure 5.26: Plots of PV/nRT versus P for nitrogen gas at three temperatures.
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Figure 5.27: (a) Gas at low concentration— relatively few interactions between particles. (b) Gas at high concentration—many more interactions between particles.
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Real Gases  
corrected pressure
corrected volume
Pideal
Videal
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